In this paper, the state of metastable equilibrium and the state of unstable equilibrium of water at a certain temperature are explored using an exact difference lattice Boltzmann model and the conditions of bubble (droplet) formation are investigated in the isothermal phase transition processes. From these simulation results, it is found that the model predictions are in good agreement with analytical results. Based on these works, a new model, which is based on exact difference lattice Boltzmann model and extended with an energy transfer equation to model heat transfer, is proposed to describe liquid-vapor phase transition process. The effects of the wall-fluid interaction strength on the bubble nucleation process in a pit are investigated using this new heterogeneous phase transition model. Simulation results accurately reproduce the characteristics of three stages of the bubble nucleation process. The changes of the contact angle, curvature radius, and volume with the bubble nucleation process are explored, and the relationship curve between curvature and bubble volume from the simulations is in qualitative agreement with the previous results.